I know cheap inner tubes can be a bother this way, they sometimes tear for no good reason. At the bike shop they have a couple of times thrown out entire boxes of bad batches of tubes, I can't remember the brand name at the moment. Try a more trusted brand next time, at least a different one. It's common to make tears in the tube when you put the tire back on, be very careful when using tyre levers. In most cases you can get the tyre back on with otu levers by pressing the walls of the tire between you fingers and making sure it settles well into the rim all round the wheel, then the last bit usually snaps into place with ease. Pump some air into a brand new tube and let it out again, it stretches it and its easier to get in place under the tyre. Most tyres with kevlar guard are acceptable, but the best this way is Schwalbe's Marathon line, I have had Marathon Pluss (optimal puncture resistance) and Marathon Green Guard. These are havier tyres, there are fimer and lighter ones like Delta Cruiser with kevlar guide.